Problem

Source: Sharygin 2023 - P16 (Grade-9-11)

Tags: geometry, reflection, altitudes, Sharygin Geometry Olympiad, Sharygin 2023



Let $AH_A$ and $BH_B$ be the altitudes of a triangle $ABC$. The line $H_AH_B$ meets the circumcircle of $ABC$ at points $P$ and $Q$. Let $A'$ be the reflection of $A$ about $BC$, and $B'$ be the reflection of $B$ about $CA$. Prove that $A',B', P,Q$ are concyclic.